I'm saving money I need in the next few years to a UK cash ISA and a regular UK saving account. Money for the longer term goes into a 60/40 mix of low expense stock/bond index funds back in the US. You must put UK interest on your 1040. You file the TDF90-22.1 if the total of your foreign accounts goes over $10k.
Assuming you're a US citizen going to school in the UK and you've been here less that 7 years out of the last 9 you'll be taxed on a remittance basis so US interest left in US accounts won't be taxed by the UK. That might be something to think about. I've been in the UK almost 3 years and I'm hoping to buy a flat soon so I'm saving for that in UK savings accounts as I don't want to deal with currency fluctuations.
To properly decide the best tax strategy you need to take into account your citizenship, residency, the level of your income, and if you are on a grant or stipend the nature of that too